Nonconvex Mixed-integer Nonlinear Programming Problem Research Articles

Optimal Coordinated Operation of Distributed Static Series Compensators for Wide-area Network Congestion Relief

Relieving network congestions is a critical goal for the safe and flexible operation of modern power systems, especially in the presence of intermittent renewables or distributed generation. This paper deals with the real-time coordinated operation of distributed static series compensators (DSSCs) to remove network congestions by suitable modifications of the branch reactance. Several objective functions are considered and discussed to minimize the number of the devices involved in the control actions, the total losses or the total reactive power exchanged, leading to a non-convex mixed-integer non-linear programming problem. Then, a heuristic methodology combining the solution of a regular NLP with k-means clustering algorithm is proposed to get rid of the binary variables, in an attempt to reduce the computational cost. The proposed coordinated operation strategy of the DSSCs is tested on several benchmark systems, providing feasible and sufficiently optimal solutions in a reasonable time frame for practical systems.

Deep Reinforcement Learning-Based Resource Allocation in Cooperative UAV-Assisted Wireless Networks

We consider the downlink of an unmanned aerial vehicle (UAV) assisted cellular network consisting of multiple cooperative UAVs, whose operations are coordinated by a central ground controller using wireless fronthaul links, to serve multiple ground user equipments (UEs). A problem of jointly designing UAVs’ positions, transmit beamforming, as well as UAV-UE association is formulated in the form of mixed integer nonlinear programming (MINLP) to maximize the sum UEs’ achievable rate subject to limited fronthaul capacity constraints. Solving the considered problem is hard owing to its non-convexity and the unavailability of channel state information (CSI) due to the movement of UAVs. To tackle these effects, we propose a novel algorithm comprising of two distinguishing features: (i) exploiting a deep Q-learning approach to tackle the issue of CSI unavailability for determining UAVs’ positions, (ii) developing a difference of convex algorithm (DCA) to efficiently solve for the UAV’s transmit beamforming and UAV-UE association. The proposed algorithm recursively solves the problem of interest until convergence, where each recursion executes two steps. In the first step, the deep Q-learning (DQL) algorithm allows UAVs to learn the overall network state and account for the joint movement of all UAVs to adapt their locations. In the second step, given the determined UAVs’ positions from the DQL algorithm, the DCA iteratively solves a convex approximate subproblem of the original non-convex MINLP problem with the updated parameters, where the problem’s variables are transmit beamforming and UAV-UE association. Numerical results show that our design outperforms the existing algorithms in terms of algorithmic convergence and network performance with a gain of up to 70%.

Energy-Efficient Parallel Multi-Access Edge Computing in OFDMA Wireless Networks

We study a parallel multi-access edge computing (MEC) system in this work and investigate its energy-efficient resources management. Particularly, the MEC system consists of an edge node and a number of mobile users, where each user has an inelastic computing task with nonnegligible duration of task execution and nonnegligible size of task result. In addition, the MEC system operates in orthogonal frequency division multiple access (OFDMA) wireless networks and can support the transmission as well as the execution of different tasks in parallel. On this basis, we build a nonconvex mixed-integer nonlinear programming (MINLP) problem aiming to minimize the energy consumed by the system. By using the McCormick method and exploring the problem's structural properties, we first equivalently transform it to a manageable convex MINLP problem, and then devise two low-complexity suboptimal algorithms. Finally, numerical results are presented to show the effectiveness of our proposed algorithms.

A MINLP approach to improve heat transfer in flat plates through the optimal distribution of nanoparticles

In this work, the thermal effect of deploying nanoparticles on the steady-state two-dimensional heat transfer behavior on a square plate is presented. The aim is to strengthen process intensification through efficient energy use. The approach of this work is to present a general methodology to obtain the optimal configuration of the nanoparticles and the base fluid respectively in the system. Here, the objective function is maximizing the heat transfer of the system considering that the performance of the nanofluids depends on the distribution of the nanoparticles. A general model is presented that allows solving the two-dimensional heat equation for the nanoparticles and the base fluid independently. The mathematical formulation is presented as a problem of Mixed-Integer Non-linear Programming (MINLP) model. The system under consideration is a mixture of metallic nano-sized particles and conventional heat-transferring fluid. In addition, it is also considered that there is heat generation inside the base fluid and as well the thermal conductivity of the flat plate is assumed to vary as a linear function of the temperature. The results indicate that improved heat transfer can be achieved through optimal fluid location. However, in few cases this behavior was not observed and the explanation of this issue is linked to the the nonconvex MINLP problem rendering only optimal local solutions. In order to show the applicability of the proposed methodology, two parametric case studies are presented.

Joint User Pairing and Resource Allocation in a SWIPT-Enabled Cooperative NOMA System

This paper studies a novel design of user pairing and resource allocation in a simultaneous wireless information and power transfer (SWIPT)-enabled cooperative non-orthogonal multiple access (NOMA) system with coexisting power-splitting (PS) and time-switching (TS) users. In this system, near NOMA users (NUs) that are close to a source can assist the communications between the source and far NOMA users (FUs) using the energy harvested by either PS or TS strategy. The design aims to maximize the sum-rate of the system by optimizing user pairing and power allocation between NUs and FUs as well as performing PS and TS control at NUs, while guaranteeing the target data rates and the minimum harvested energy requirements of users. Since the joint design is formulated as a non-convex mixed-integer non-linear programming (MINLP) problem that is challenging to tackle, we propose a two-step user pairing and resource allocation algorithm. Specifically, we decouple the original problem into an inner resource allocation problem and an outer user pairing problem. For the inner problem, we propose successive convex approximation (SCA) and block coordinate descent (BCD)-based algorithms to perform power allocation as well as PS and TS control iteratively, with the algorithms’ convergence being theoretically proved. By exploiting the characteristics of the outer problem of user pairing, this problem is well tackled by the Hungarian algorithm. Simulation results demonstrate the proposed joint design yields better performance gains than the existing schemes.

Efficient Resource Allocation Using Distributed Edge Computing in D2D Based 5G-HCN With Network Slicing

Fifth Generation (5G) cellular networks aim to overcome the pressing demands posed by dynamic Quality of Service (QoS) constraints, which have primarily remained unaddressed using conventional network infrastructure. Cellular networks of the future necessitate the formulation of efficient resource allocation schemes that readily meet throughput requirements. The idea of combining Device-to-Device (D2D), Mobile Edge Computing (MEC), and Network slicing (NS) can improve spectrum utilization with better performance and scalability. This work presents a spectrum efficiency optimization problem in D2D based 5G-Heterogeneous Cellular Network (5G-HCN) with NS. Owing to the shortage of resources, we propose an underlay model where macro-cell users (MUs), small-cell users (SUs), and D2D users (DUs) reuse the resources while considering the effects of interference. The goal is to maximize the average network spectrum efficiency (SE) and throughput without degrading the system performance. The problem at hand is naturally a non-convex mixed-integer non-linear programming (MINLP) problem that is intractable. Therefore, we have suggested a distributed resource allocation strategy with an edge computing (DRA-EC) approach to find the sub-optimal solution. In distributed augmented Lagrange method, each edge router located at BS will solve its problem locally, and the consensus algorithm will find the global solution using these local estimates. The central slice controller will cut the customized network slices according to the bandwidth requirements of each user type with optimized spectrum information. The simulation outcomes prove that our proposed method is near the central optimization scheme with low computational complexity. It is much better because it reduces the computational time and system overhead.

Minotaur: a mixed-integer nonlinear optimization toolkit

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting extensions that we implement in our framework and demonstrate their impact on solution times. Without a flexible framework that enables structure exploitation, finding global solutions to difficult nonconvex MINLP problems will remain out of reach for many applications.

Practical approximations and heuristic approaches for managing shiftable loads in the multi-period optimal power flow framework

The presence of smart buildings (SBs) is expected to grow manifold in the next decade, leading to both challenges and opportunities in managing increasingly “active” distribution systems. SBs are host to a number of devices and technologies capable of providing residential flexibility in order to maintain acceptable operating conditions within the distribution system. A prevalent class of devices with significant potential for flexibility provision are shiftable loads (SLs), which represent a large amount of potential SB-provided flexibility. However, the accurate modelling of SLs within the multi-period optimal power flow (MP-OPF) framework results in complex non-convex mixed-integer nonlinear programming (MINLP) problems. For realistic feeders, MINLP problems are intractable and hence require some heuristic form of circumvention. This work evaluates the limitations of the MINLP formulation and proposes new practical alternatives, namely a flexible NLP approximation and a multi-faceted heuristic algorithm. The proposed approaches are generic and applicable for any problem size or type of SL, while they are shown to work efficiently, both speed-wise and solution-quality-wise, outperforming state-of-the-art MINLP solvers. A simple scoring and ranking scheme is also proposed in order to make a direct comparison between the different approaches.

Intelligent Offloading for NOMA-Assisted MEC via Dual Connectivity

Multiaccess edge computing (MEC), which brings computing capability close to the user equipment (UE) within a radio access network (RAN), is a promising technique to meet the challenges of explosive growth in edge data traffic and the number of connected devices. Nevertheless, MEC offloading failures, i.e., interruption of task offloading due to UE mobility and limited battery capacity, are still an important issue. In this article, we aim to minimize the total energy consumption in dual connectivity (DC)- and nonorthogonal multiple access (NOMA)-assisted computation offloading systems. This problem is formulated as a mixed-integer nonlinear programming (MINLP) problem with nonconvex constraints, which is a nondeterministic polynomial-time (NP)-hard and perplexing problem. To address this problem, we propose an iterative optimization algorithm to obtain a suboptimal time scheduling and task allocation solution. Specifically, we solve the nonconvex constrained MINLP problems by exploiting the successive convex approximation (SCA) algorithm and the nonlinear optimization algorithm with the mesh adaptive direct search (MADS) (NOMAD). Furthermore, a deep learning-based intelligent offloading scheme is introduced, called a cyclic branch network, to fully utilize data traffic and the computing capability on the network edge. Numerical results show that the proposed intelligent offloading scheme has comparable performance and dramatically reduces the inference time compared with the traditional optimization algorithm.

Resource allocation for energy efficient user association in user-centric ultra-dense networks integrating NOMA and beamforming

A coupling of wireless access via non-orthogonal multiple access and wireless backhaul via beamforming is a promising way for downlink user-centric ultra-dense networks (UDNs) to improve system performance. However, ultra-dense deployment of radio access points in macrocell and user-centric view of network design in UDNs raise important concerns about resource allocation and user association, among which notably is energy efficiency (EE) balance. To overcome this challenge, we develop a framework to investigate the resource allocation problem for energy efficient user association in such a scenario. The joint optimization framework aiming at the system EE maximization is formulated as a large-scale non-convex mixed-integer nonlinear programming problem, which is NP-hard to solve directly with lower complexity. Alternatively, taking advantages of sum-of-ratios decoupling and successive convex approximation methods, we transform the original problem into a series of convex optimization subproblems. Thenwe solve each subproblem through Lagrangian dual decomposition, and design an iterative algorithm in a distributed way that realizes the joint optimization of power allocation, sub-channel assignment, and user association simultaneously. Simulation results demonstrate the effectiveness and practicality of our proposed framework, which achieves the rapid convergence speed and ensures a beneficial improvement of system-wide EE.

Relay Selection, Scheduling, and Power Control in Wireless-Powered Cooperative Communication Networks

Relay nodes are used to improve the throughput, delay and reliability performance of energy harvesting networks by assisting both energy and information transfer between sources and access point. Previous studies on radio frequency energy harvesting networks are limited to single-source-single/multiple-relay networks. In this paper, a novel joint relay selection, scheduling and power control problem for multiple-source-multiple-relay network is formulated with the objective of minimizing the total duration of wireless power and information transfer. The formulated problem is non-convex mixed-integer non-linear programming problem, and proven to be NP-hard. We first formulate a sub-problem on scheduling and power control for a given relay selection. We propose an efficient optimal algorithm based on a bi-level optimization over power transfer time allocation. Then, for optimal relay selection, we present optimal exponential-time Branch-and-Bound (BB) based algorithm where the nodes are pruned with problem specific lower and upper bounds. We also provide two BB-based heuristic approaches limiting the number of branches generated from a BB-node, and a relay criterion based lower complexity heuristic algorithm. The proposed algorithms are demonstrated to outperform conventional harvest-then-cooperate approaches with up to 87% lower schedule length for various network settings with at least 7.88 times higher algorithm runtime.

Joint Optimal Software Caching, Computation Offloading and Communications Resource Allocation for Mobile Edge Computing

As software may be used by multiple users, caching popular software at the wireless edge has been considered to save computation and communications resources for mobile edge computing (MEC). However, fetching uncached software from the core network and multicasting popular software to users have so far been ignored. Thus, existing design is incomplete and less practical. In this paper, we propose a joint caching, computation and communications mechanism which involves software fetching, caching and multicasting, as well as task input data uploading, task executing (with non-negligible time duration) and computation result downloading, and mathematically characterize it. Then, we optimize the joint caching, offloading and time allocation policy to minimize the weighted sum energy consumption subject to the caching and deadline constraints. The problem is a challenging two-timescale mixed integer nonlinear programming (MINLP) problem, and is NP-hard in general. We convert it into an equivalent convex MINLP problem by using some appropriate transformations and propose two low-complexity algorithms to obtain suboptimal solutions of the original non-convex MINLP problem. Specifically, the first suboptimal solution is obtained by solving a relaxed convex problem using the consensus alternating direction method of multipliers (ADMM), and then rounding its optimal solution properly. The second suboptimal solution is proposed by obtaining a stationary point of an equivalent difference of convex (DC) problem using the penalty convex-concave procedure (Penalty-CCP) and ADMM. Finally, by numerical results, we show that the proposed solutions outperform existing schemes and reveal their advantages in efficiently utilizing storage, computation and communications resources.

Joint Optimization of Energy-Harvesting-Powered Two-Way Relaying D2D Communication for IoT: A Rate–Energy Efficiency Tradeoff

Device-to-device (D2D) communication is a key enabling technology to facilely realizing the Internet of Things (IoT) due to its spectral and energy efficiencies features. Exploiting the physical-layer network coding (PNC) and energy harvesting (EH) technology, two-way relaying (TWR) D2D communication can achieve significant performance for IoT in terms of data rate and energy efficiency (EE). In this article, we investigate the EH-aided TWR D2D communication sharing the uplink (UL) spectrum of the traditional cellular networks. We assume that the D2D transmitters, receivers, and participating relays can collect renewable energy (RE) from natural resources. Also, the relays are considered to be powered by radio-frequency (RF) signals utilizing the power splitting (PS) protocol. Subject to the Quality of Service (QoS), power, subchannel assignment, EH, and maximum practical power constraints, two nonconvex mixed-integer nonlinear programming (MINLP) problems are formulated. The two problems provide a tradeoff on either maximizing the TWR D2D link (TDL) rate or its EE depending on the IoT application needs. Based on the particle swarm optimization (PSO) algorithm, we propose the rate and EE tradeoff EH-based algorithm (REET-EH) to deal with these problems. The proposed algorithm can optimally perform the resource allocation (RA), PS factors determination, power allocation (PA), and relay selection processes. The numerical results investigate the performance of the REET-EH algorithm and show its consistency over several parameters. Also, the results illustrate that our proposed algorithm improves the system performance compared with other state-of-the-art algorithms with regard to the D2D link rate and EE.

Energy-Efficient Resource Allocation for High-Rate Underlay D2D Communications With Statistical CSI: A One-to-Many Strategy

For the prominent superiorities in energy and spectrum efficiency, Device-to-Device (D2D) communication has become a hot topic among the 5th generation (5G) technologies. However, the widely adopted mode that one or more D2D links reuse one cellular user‘s uplink spectrum may lead to severe limitation on D2D communication rate, especially when cellular user's uplink spectrum is very limited. In this paper, we will face the high rate requirements of D2D pairs (DPs), with the help of carrier aggregation technology, each DP can reuse the uplink spectrum of multiple cellular users when needed. More practically, we consider that only statistical channel state information (CSI) of certain communication links is available here. Then, we formulate the problem to minimize the total power consumption of the mobile devices to obtain an energy-efficient resource allocation result, including spectrum and power allocation. Meanwhile, the quality of service (QoS) requirements of cellular and high-rate D2D communications are both ensured. The formulated problem is mathematically a non-convex mixed-integer nonlinear programming (MINLP) problem, which is NP-hard. To solve it, we first tighten the constraints and deploy transformation methods on it to make it convex. Then, we propose a two-layer algorithm, the independent-power greedy-based outer approximation (IPGOA), to solve the transformed problem. Besides, to handle the involved uniform power allocation circumstance in the carrier aggregation process, a uniform-power GOA (UPGOA) algorithm, which can be regarded as a simplified version of IPGOA, is also proposed. The simulation results show that in different scenarios, our proposed scheme is approximately optimal.

Altruistic Control of Connected Automated Vehicles in Mixed-Autonomy Multi-Lane Highway Traffic

We consider the problem of altruistic control of connected automated vehicles (CAVs) on mixed-autonomy multi-lane highways to mitigate moving traffic jams resulting from car-following dynamics of human-driven vehicles (HDVs). In most of the existing studies on CAVs in multi-lane settings, vehicle controller design philosophy is based on a selfish driving strategy that exclusively addresses the ego vehicle objectives. To improve overall traffic smoothness, we propose an altruistic control strategy for CAVs that aims to maximize the driving comfort and traffic efficiency of both the ego vehicle and surrounding HDVs. We formulate the problem of altruistic control under a model predictive control (MPC) framework to optimize acceleration and lane change sequences of CAVs. In order to efficiently solve the resulting non-convex mixed-integer nonlinear programming (MINLP) problem, we decompose it into three non-convex subproblems, each of which can be transformed into a convex quadratic program via penalty based reformulation of the optimal velocity with relative velocity (OVRV) car-following model. Simulation results demonstrate significant improvements in traffic flow via altruistic CAV actions over selfish strategies on both single- and multi-lane roads.

A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs

This paper proposes a joint decomposition method that combines Lagrangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search. In this approach, we view the variables coupling the scenario dependent variables and those causing nonconvexity as complicating variables. We systematically solve the Lagrangian decomposition subproblems and the generalized Benders decomposition subproblems in a unified framework. The method requires the solution of a difficult relaxed master problem, but the problem is only solved when necessary. Enhancements to the method are made to reduce the number of the relaxed master problems to be solved and ease the solution of each relaxed master problem. We consider two scenario-based, two-stage stochastic nonconvex MINLP problems that arise from integrated design and operation of process networks in the case study, and we show that the proposed method can solve the two problems significantly faster than state-of-the-art global optimization solvers.

Carbon-neutral hybrid energy systems with deep water source cooling, biomass heating, and geothermal heat and power

This article addresses the optimal design of carbon-neutral hybrid energy system with deep water source cooling, biomass heating, and geothermal heat and power. A novel superstructure of the proposed hybrid energy system comprised of an enhanced geothermal system, a torrefied biomass-based combustion system, and a deep water source cooling system with conventional chillers as auxiliaries, is developed. Based on the superstructure of the proposed hybrid energy system, we develop a multi-period optimization model to minimize a fractional metric, the levelized cost. Because the main product of the hybrid energy system is heat, the levelized cost is expressed as levelized cost of heat, with other byproducts indirectly incorporated by using credits. The resulting nonconvex mixed-integer nonlinear fractional programming problem is efficiently solved by using a tailored optimization algorithm. Two case studies based on Cornell’s campus in Ithaca, New York are presented to quantify the effect of different electric power sources on the technoeconomic objective, as well as the life cycle greenhouse gas emissions. The first case study considers electric power from natural gas, while a carbon-neutral electric power supply based on renewable geothermal energy is envisioned in the second case study. Results show that switching the electric power supply from natural gas to geothermal energy could reduce the greenhouse gas emissions by 24.5%, while only increasing the levelized cost of heat by 5.6%. The carbon footprint for both case studies are promisingly low, compared with numerous existing heat generation technologies. Through sensitivity analysis, the project lifetime is identified as the most influential input parameter.

Coordinated Operation of Electricity and Natural Gas Systems: A Convex Relaxation Approach

The variability in the generation dispatch of the natural gas generation units will lead to fluctuation in natural gas demand profile that could further jeopardize the security of the natural gas network. The coordinated operation of electricity and natural gas infrastructure systems would help to improve the security and reliability measures in both infrastructure systems and mitigate the risk of demand curtailment. The electricity and natural gas network operation problems are non-convex mixed-integer nonlinear programming problems that are hard to solve in polynomial time. The non-convex feasible regions are formed by the Weymouth constraint and the introduced binary commitment decision variables in the natural gas and electricity network operation problems, respectively. This paper utilized a sparse semidefinite programming (SDP) relaxation to procure the optimal solution for the coordinated operation of electricity and natural gas networks. The presented algorithm leverages the sparseness of the natural gas network to construct several small matrices of lifting variables that are used to form a tight and traceable SDP relaxation. A set of valid constraints that tighten the relaxation ensures the exactness of the solution procured from the relaxed problem. The effectiveness of the presented approach is shown in case studies.

Energy-efficient multi-cell resource allocation in cognitive radio-enabled 5G systems

In this paper, we propose an energy-efficient resource allocation (RA) algorithm in cognitive radio-enabled 5th generation (5G) systems, where the scenario including one primary system and multiple secondary cells is considered. Because of the high spectrum leakage of traditional orthogonal frequency division multiplexing (OFDM), alternative modulation schemes regarded as the potential air interfaces in 5G are analyzed, e.g., filter bank-based multi-carrier (FBMC), generalized frequency division multiplexing (GFDM), and universal filtered multi-carrier (UFMC). Our objective is to maximize the whole energy efficiency of secondary system defined by the ratio of the capacity to the total power consumption subject to some practical constraints. The general formulation leads to a non-convex mixed-integer nonlinear programming problem with fractional structure, which is challenging to solve due to its intractability and significant complexity. Therefore, we resort to an alternate optimization framework to optimize the variables of subcarrier assignment and power allocation, where successive convex approximation (SCA) is employed so that the general formulation is finally transformed into a solvable convex problem. Numerical results validate the effectiveness of the proposed RA algorithm, and the comparison with some existing RA algorithms is conducted. In addition, the performance of using different 5G candidate waveforms in the energy-efficient RA algorithm is also presented and discussed.

Channel selection and power allocation for device‐to‐device enabled cellular networks

Cellular networks with device-to-device (D2D) communication capabilities offer increased spectrum utilisation and system throughput. However, these performance gains depend on the channel and power allocation strategy used. In this study, the authors have chosen underlay D2D as it is more advantageous in terms of spectrum efficiency, but introduces additional interferences. To cope up with these challenges, they propose new channel assignment and power allocation schemes with and without Quality of Service (QoS) constraint for D2D pairs. The authors' schemes allow multiple channels to be shared by each D2D pair without degrading the performance of the existing cellular system. First, they formulate the joint channel and power allocation problem without considering the QoS for D2D pairs which results in a non-convex mixed-integer non-linear programming problem and cannot be solved in polynomial time. Then, the problem of channel and power allocation is reformulated and optimised, individually. Following this, they introduce QoS constraints for each D2D pair by specifying the minimum number of channels that should be allocated to each D2D pair during the assignment. The effectiveness of their scheme is verified through numerical results.